Subgroups — C₁₃×#19904 #15706243

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1708	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1701	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1684	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1631	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1624	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#555	C₂²	1	1	yes	characteristic
17	C₁₃×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#547	C₂²	1	1	yes	characteristic
20	C₁₃×#498	C₂²	1	1	yes	characteristic
21	C₁₃×#492	C₂²	1	1	yes	characteristic
22	C₁₃×#487	C₂²	1	1	yes	characteristic
23	C₁₃×#487	C₂²	1	1	yes	characteristic
24	C₁₃×#486	—	2	1	no	—
25	C₁₃×#486	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#485	—	2	1	no	—
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#481	—	2	1	no	—
30	C₁₃×#477	C₂²	1	1	yes	characteristic
31	C₁₃×#476	C₂²	1	1	yes	characteristic
32	C₁₃×#475	C₂²	1	1	yes	characteristic
33	C₁₃×#474	—	2	1	no	—
34	C₁₃×#474	C₂²	1	1	yes	characteristic
35	C₁₃×#469	—	2	1	no	—
36	C₁₃×#468	—	2	1	no	—
37	C₁₃×#465	—	2	1	no	—
38	C₁₃×#461	C₂²	1	1	yes	characteristic
39	C₁₃×#461	C₂²	1	1	yes	characteristic
40	C₁₃×#459	—	2	1	no	—
41	C₁₃×#459	C₂²	1	1	yes	characteristic
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#449	—	2	1	no	—
44	C₁₃×#449	—	2	1	no	—
45	C₁₃×#448	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×D₈	—	2	1	no	—
49	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
50	C₁₃×#436	C₂²	1	1	yes	characteristic
51	C₁₃×#436	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₁₃×#419	—	2	1	no	—
54	C₁₃×#417	—	2	1	no	—
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₁₃	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×#41	—	2	1	no	—
69	C₂²×Q₈×C₁₃	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	4	1	no	—
73	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
74	C₂×C₁₃×D₈	—	2	1	no	—
75	C₂×C₁₃×D₈	—	2	1	no	—
76	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	—	2	1	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×#127	—	2	1	no	—
85	C₁₃×#127	C₂³	1	1	yes	characteristic
86	C₁₃×#124	—	4	1	no	—
87	C₁₃×#123	—	4	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×C₂²⋊Q₈	—	4	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	4	1	no	—
96	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#117	—	2	1	no	—
103	C₁₃×#117	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	D₄	1	1	yes	characteristic
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	—	4	1	no	—
111	C₁₃×#106	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	—	2	1	no	—
113	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×#103	—	2	1	no	—
118	C₁₃×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	D₄	1	1	yes	characteristic
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	D₄	1	1	yes	characteristic
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19904	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	4	2	no	—
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	8	1	no	—
148	C₁₃×#41	—	8	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	4	1	no	—
153	C₂×Q₈×C₁₃	—	4	2	no	—
154	C₂×Q₈×C₁₃	—	8	1	no	—
155	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	4	1	no	—
160	C₂×D₄×C₁₃	—	4	1	no	—
161	C₂×D₄×C₁₃	—	4	1	no	—
162	C₂×D₄×C₁₃	—	4	1	no	—
163	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	4	1	no	—
170	C₂²×C₄×C₁₃	—	4	1	no	—
171	C₂²×C₄×C₁₃	—	4	1	no	—
172	C₁₃×SD₁₆	—	2	2	no	—
173	C₁₃×SD₁₆	—	8	2	no	—
174	C₁₃×SD₁₆	—	8	1	no	—
175	C₁₃×SD₁₆	—	8	1	no	—
176	C₁₃×D₈	—	4	1	no	—
177	C₁₃×D₈	—	4	2	no	—
178	C₁₃×D₈	—	8	1	no	—
179	C₁₃×M₁₆	—	8	1	no	—
180	C₁₃×M₁₆	—	8	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	8	1	no	—
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	4	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₁₃×C₂²⋊C₄	—	4	1	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	4	1	no	—
214	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
215	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3332	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3329	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1708	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1703	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1701	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1684	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1681	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1654	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1651	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1631	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1624	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1589	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	8	2	no	—
240	Q₈×C₁₃	—	8	1	no	—
241	Q₈×C₁₃	#135	1	2	yes	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	2	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	8	2	no	—
253	D₄×C₁₃	—	8	1	no	—
254	D₄×C₁₃	—	8	2	no	—
255	D₄×C₁₃	—	16	1	no	—
256	D₄×C₁₃	—	16	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	8	2	no	—
272	C₂×C₄×C₁₃	—	8	2	no	—
273	C₂×C₄×C₁₃	—	8	2	no	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
277	C₈×C₁₃	—	2	2	no	—
278	C₈×C₁₃	—	2	1	no	—
279	C₈×C₁₃	—	2	1	no	—
280	C₈×C₁₃	—	2	1	no	—
281	C₈×C₁₃	—	2	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₈×C₁₃	—	4	1	no	—
285	C₈×C₁₃	—	4	1	no	—
286	#555	C₂²×C₁₃	1	1	yes	characteristic
287	#550	C₂²×C₁₃	1	1	yes	characteristic
288	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
289	#547	C₂²×C₁₃	1	1	yes	characteristic
290	#498	C₂²×C₁₃	1	1	yes	characteristic
291	#492	C₂²×C₁₃	1	1	yes	characteristic
292	#487	C₂²×C₁₃	1	1	yes	characteristic
293	#487	C₂²×C₁₃	1	1	yes	characteristic
294	#486	—	2	1	no	—
295	#486	C₂²×C₁₃	1	1	yes	characteristic
296	#486	C₂²×C₁₃	1	1	yes	characteristic
297	#485	—	2	1	no	—
298	#485	—	2	1	no	—
299	#481	—	2	1	no	—
300	#477	C₂²×C₁₃	1	1	yes	characteristic
301	#476	C₂²×C₁₃	1	1	yes	characteristic
302	#475	C₂²×C₁₃	1	1	yes	characteristic
303	#474	—	2	1	no	—
304	#474	C₂²×C₁₃	1	1	yes	characteristic
305	#469	—	2	1	no	—
306	#468	—	2	1	no	—
307	#465	—	2	1	no	—
308	#461	C₂²×C₁₃	1	1	yes	characteristic
309	#461	C₂²×C₁₃	1	1	yes	characteristic
310	#459	—	2	1	no	—
311	#459	C₂²×C₁₃	1	1	yes	characteristic
312	#459	C₂²×C₁₃	1	1	yes	characteristic
313	#449	—	2	1	no	—
314	#449	—	2	1	no	—
315	#448	—	2	1	no	—
316	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
318	C₄×D₈	—	2	1	no	—
319	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
320	#436	C₂²×C₁₃	1	1	yes	characteristic
321	#436	C₂²×C₁₃	1	1	yes	characteristic
322	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
323	#419	—	2	1	no	—
324	#417	—	2	1	no	—
325	#416	—	2	1	no	—
326	#335	C₂²×C₁₃	1	1	yes	characteristic
327	#334	C₂²×C₁₃	1	1	yes	characteristic
328	#333	C₂²×C₁₃	1	1	yes	characteristic
329	#332	C₂²×C₁₃	1	1	yes	characteristic
330	#332	C₂²×C₁₃	1	1	yes	characteristic
331	#331	C₂²×C₁₃	1	1	yes	characteristic
332	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
333	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₈²	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	D₄²	1	1	yes	characteristic
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	—	8	1	no	—
359	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
360	C₄×C₁₃	#575	1	1	yes	characteristic
361	C₄×C₁₃	#576	1	1	yes	characteristic
362	C₄×C₁₃	#577	1	1	yes	characteristic
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂²×Q₈	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	4	1	no	—
369	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
370	C₂×D₈	—	2	1	no	—
371	C₂×D₈	—	2	1	no	—
372	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₄⋊Q₈	—	2	1	no	—
377	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
380	#127	—	2	1	no	—
381	#127	C₂³×C₁₃	1	1	yes	characteristic
382	#124	—	4	1	no	—
383	#123	—	4	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	4	1	no	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	4	1	no	—
392	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	#107	—	2	1	no	—
402	#107	—	2	1	no	—
403	#107	D₄×C₁₃	1	1	yes	characteristic
404	#106	—	2	1	no	—
405	#106	—	2	1	no	—
406	#106	—	4	1	no	—
407	#106	D₄×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	D₄×C₁₃	1	1	yes	characteristic
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	D₄×C₁₃	1	1	yes	characteristic
431	#102	D₄×C₁₃	1	1	yes	characteristic
432	#102	D₄×C₁₃	1	1	yes	characteristic
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₁₃	—	8	1	no	—
441	C₂×C₁₃	—	8	1	no	—
442	C₂×C₁₃	—	8	1	no	—
443	C₂×C₁₃	—	16	1	no	—
444	C₂×C₁₃	#3275	1	1	yes	characteristic
445	C₂×C₁₃	#3280	1	1	yes	characteristic
446	C₂×C₁₃	#3291	1	1	yes	characteristic
447	#41	—	4	2	no	—
448	#41	—	4	2	no	—
449	#41	—	8	1	no	—
450	#41	—	8	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	4	1	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	8	1	no	—
457	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	SD₁₆	—	2	2	no	—
475	SD₁₆	—	8	2	no	—
476	SD₁₆	—	8	1	no	—
477	SD₁₆	—	8	1	no	—
478	D₈	—	4	1	no	—
479	D₈	—	4	2	no	—
480	D₈	—	8	1	no	—
481	M₁₆	—	8	1	no	—
482	M₁₆	—	8	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	8	1	no	—
489	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	4	1	no	—
516	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₁₃	#19904	1	1	yes	characteristic, direct product factor, Sylow
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	4	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	8	2	no	—
528	Q₈	—	8	1	no	—
529	Q₈	C₁₃×#135	1	2	yes	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	2	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	8	2	no	—
541	D₄	—	8	1	no	—
542	D₄	—	8	2	no	—
543	D₄	—	16	1	no	—
544	D₄	—	16	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
565	C₈	—	2	2	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	D₄²×C₁₃	1	1	yes	characteristic
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
597	C₄	C₁₃×#575	1	1	yes	characteristic
598	C₄	C₁₃×#576	1	1	yes	characteristic
599	C₄	C₁₃×#577	1	1	yes	characteristic
600	C₂	—	8	1	no	—
601	C₂	—	8	1	no	—
602	C₂	—	8	1	no	—
603	C₂	—	16	1	no	—
604	C₂	C₁₃×#3275	1	1	yes	characteristic
605	C₂	C₁₃×#3280	1	1	yes	characteristic
606	C₂	C₁₃×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3358	C₂	semidirect
2. C₁₃×#3332	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3303	C₂	semidirect
5. C₁₃×#1708	C₂	semidirect
6. C₁₃×#1703	C₂	semidirect
7. C₁₃×#1701	C₂	semidirect
8. C₁₃×#1684	C₂	semidirect
9. C₁₃×#1681	C₂	semidirect
10. C₁₃×#1654	C₂	semidirect
11. C₁₃×#1651	C₂	semidirect
12. C₁₃×#1631	C₂	semidirect
13. C₁₃×#1624	C₂	semidirect
14. C₁₃×#1589	C₂	semidirect
15. C₈×C₁₃×SD₁₆	C₂	semidirect
144. #19904	C₁₃	direct (N × H)
215. #3358	C₂×C₁₃	semidirect
216. #3332	C₂×C₁₃	semidirect
217. #3329	C₂×C₁₃	semidirect
218. #3303	C₂×C₁₃	semidirect
219. #1708	C₂×C₁₃	semidirect
220. #1703	C₂×C₁₃	semidirect
221. #1701	C₂×C₁₃	semidirect
222. #1684	C₂×C₁₃	semidirect
223. #1681	C₂×C₁₃	semidirect
224. #1654	C₂×C₁₃	semidirect
225. #1651	C₂×C₁₃	semidirect
226. #1631	C₂×C₁₃	semidirect
227. #1624	C₂×C₁₃	semidirect
228. #1589	C₂×C₁₃	semidirect
229. C₈×SD₁₆	C₂×C₁₃	semidirect
517. C₁₃	#19904	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3358	2
C₁₃×#3332	2
C₁₃×#3329	2
C₁₃×#3303	2
C₁₃×#1708	2
C₁₃×#1703	2
C₁₃×#1701	2
C₁₃×#1684	2
C₁₃×#1681	2
C₁₃×#1654	2
C₁₃×#1651	2
C₁₃×#1631	2
C₁₃×#1624	2
C₁₃×#1589	2
C₈×C₁₃×SD₁₆	2
#19904	13

Subgroups — C13×#19904 #15706243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19904 #15706243